--- title: The peak pattern puzzle keywords: fastai sidebar: home_sidebar summary: "Matching peak patterns " description: "Matching peak patterns " nb_path: "notebooks/50_peak-pattern-puzzle.ipynb" ---
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We now arrive at the central problem of MA-XRF analysis. Given a spectrum with some peaks, and given the theoretical emission peak patterns for different chemical elements, which chemical elements are present in the sample? This is what I call the peak pattern puzzle.

It is important to note that not all peaks are always due to the actual emission of chemical elements present in the scanned object. Other peaks are generated by the instrument itself. And small peaks can also just be noise. Instrument peaks are common to all spectra. For example, the large peak observed in all spectra near zero energy is a result of the instrument detector physics. Other peaks above 18 keV are due emission and subsequent scattering of the rhodium anode present in the x-ray tube.

In order to plot an overview of emission patterns import plot_patterns(). To simplify our analysis let's exclude the light elements and rare elements that we will not find in drawings.

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from maxrf4u import get_patterns, plot_patterns 
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from maxrf4u import all_elements 

# elements of interest 
# adapt selection by (un)commenting  
'''
all_elements = ['#H', '#He', '#Li', '#Be', '#B', '#C', 'N', 'O', 'F', 'Ne', 'Na', 'Mg', 
                'Al', 'Si', 'P', 'S', 'Cl', '#Ar', 'K', 'Ca', '#Sc', 'Ti', 'V', 'Cr', 
                'Mn', 'Fe', 'Co', 'Ni', 'Cu', 'Zn', '#Ga', '#Ge', 'As', '#Se', 'Br', 
                '#Kr', '#Rb', 'Sr', '#Y', '#Zr', '#Nb', '#Mo', '#Tc', '#Ru', 'Rh', '#Pd', 
                'Ag', 'Cd', '#In', 'Sn', '#Sb', '#Te', 'I', '#Xe', '#Cs', 'Ba', '#La', '#Hf', 
                '#Ta', '#W', '#Re', '#Os', '#Ir', '#Pt', '#Au', 'Hg', '#Tl', 'Pb', '#Bi', 
                '#Po', '#At', '#Rn', '#Fr', '#Ra', '#Ac', '#Rf', '#Db', '#Sg', '#Bh', '#Hs', 
                '#Mt', '#Ds', '#Rg', '#Cn', '#Nh', '#Fl', '#Mc', '#Lv', '#Ts', '#Og']
'''

elements = [elem for elem in all_elements if not '#' in elem]

print('elements = ', elements)
elements =  ['N', 'O', 'F', 'Ne', 'Na', 'Mg', 'Al', 'Si', 'P', 'S', 'Cl', 'K', 'Ca', 'Ti', 'V', 'Cr', 'Mn', 'Fe', 'Co', 'Ni', 'Cu', 'Zn', 'As', 'Br', 'Sr', 'Rh', 'Ag', 'Cd', 'Sn', 'I', 'Ba', 'Hg', 'Pb']
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plot_patterns(); 
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In the previous section, out of one million spectra, we have cherry picked 22 hotmax spectra and within each spectrum detected potentially significant peaks exceeding the Poisson noise level. We can now proceed to solve the peak pattern puzzle for each hotmax spectrum. In other words, for each spectrum explain the presence of each significant (numbered) peak. Can we attribute a given peak to a specific chemical element, the instrument or noise?

In other words, we can start to 'explain away' all peaks. It is highly instructive to walk through some interesting hotmax spectra and see which element patterns explain the peak patterns that we observe. To do so, import the plot_puzzle() function.

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from maxrf4u import plot_puzzle, plot_ptrn 
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fig, ax_ptrns, ax_spectr = plot_puzzle('RP-T-1898-A-3689.datastack', 0, color_select=['Ca'])
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In the puzzle plot for hotmax spectrum #0 above, beside instrument peaks, all other peaks are rather small. I would say that only sub peak [4] can be explained as the $K_{\alpha}$ emission of calcium.

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plot_puzzle('RP-T-1898-A-3689.datastack', 2, color_select=['Pb', 'Ca', 'Fe']);
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In hotmax spectrum #2 above, one can see that sub peaks [0], [1], [3] and [6] can all be explained by the emission of lead (Pb). The tiny peaks [8] and [9] are explained by respectively iron (Fe) and calcium (Ca).

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plot_puzzle('RP-T-1898-A-3689.datastack', 3, color_select=['Cl', 'Ca', 'Fe', 'Zn']);
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In hotmax spectrum #3 sub peak [3] interestingly indicates the presence of chlorine (Cl). Furthermore we find evidence for calcium (Ca), iron (Fe), and perhaps zinc (Zn).

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n = 0
ax0, ax1 = plot_puzzle(hma, n) 

# patterns 
plot_ptrn('Ca', -1, ax1);
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n = 1
ax0, ax1 = plot_puzzle(hma, n) 

# patterns 
plot_ptrn('O', -1, ax1);
plot_ptrn('Ca', -1, ax1);
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n = 2
ax0, ax1 = plot_puzzle(hma, n)


# patterns 
plot_ptrn('Pb', -1, ax1);
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n = 3
ax0, ax1 = plot_puzzle(hma, n)

# patterns 
plot_ptrn('Cl', -1, ax1);
plot_ptrn('Ca', -1, ax1);
plot_ptrn('Fe', -2, ax1);
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n = 4
ax0, ax1 = plot_puzzle(hma, n)

# patterns 
plot_ptrn('Fe', -3, ax1)
plot_ptrn('Ca', -1, ax1)
plot_ptrn('O', -1, ax1)
plot_ptrn('S', -1, ax1)
plot_ptrn('K', -2, ax1);
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n = 5
ax0, ax1 = plot_puzzle(hma, n)

# patterns 
plot_ptrn('Ca', -1, ax1);
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n = 6
ax0, ax1 = plot_puzzle(hma, n)

# patterns 
plot_ptrn('Ca', -1, ax1);
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n = 7
ax0, ax1 = plot_puzzle(hma, n)

# patterns 
plot_ptrn('Fe', -1, ax1);
plot_ptrn('Ti', -2, ax1);
plot_ptrn('Ca', -3, ax1);
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n = 8
ax0, ax1 = plot_puzzle(hma, n)

# patterns 
plot_ptrn('Fe', -3, ax1);
plot_ptrn('Ba', -1, ax1);
plot_ptrn('Ca', -2, ax1);
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n = 9
ax0, ax1 = plot_puzzle(hma, n)

# patterns 
plot_ptrn('Mn', -1, ax1);
plot_ptrn('Ca', -2, ax1);
plot_ptrn('Fe', -3, ax1);
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n = 10
ax0, ax1 = plot_puzzle(hma, n)

# patterns 
plot_ptrn('Fe', -1, ax1);
plot_ptrn('Ca', -2, ax1);
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The tiny peak [6] in hotmax spectrum #10 is clearly the escape peak for Fe located at 6.40 keV minus 1.74 keV.

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n = 11
ax0, ax1 = plot_puzzle(hma, n)

# patterns 
plot_ptrn('Fe', -1, ax1);
plot_ptrn('Ca', -2, ax1);
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n = 12
ax0, ax1 = plot_puzzle(hma, n)

# patterns 
plot_ptrn('Cu', -1, ax1);
plot_ptrn('Zn', -2, ax1);
plot_ptrn('Ca', -3, ax1);
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n = 13
ax0, ax1 = plot_puzzle(hma, n)

# patterns 
plot_ptrn('Cu', -1, ax1);
plot_ptrn('Zn', -2, ax1);
plot_ptrn('Ca', -3, ax1);
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n = 14
ax0, ax1 = plot_puzzle(hma, n)

# patterns 
plot_ptrn('Cu', -1, ax1);
plot_ptrn('Zn', -2, ax1);
plot_ptrn('Ca', -3, ax1);
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n = 15
ax0, ax1 = plot_puzzle(hma, n)

# patterns 
plot_ptrn('Pb', -1, ax1);
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n = 16
ax0, ax1 = plot_puzzle(hma, n)

# patterns 
plot_ptrn('Pb', -1, ax1);
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n = 17
ax0, ax1 = plot_puzzle(hma, n)

# patterns 
plot_ptrn('Ca', -1, ax1);
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n = 18
ax0, ax1 = plot_puzzle(hma, n)

# patterns 
plot_ptrn('Pb', -1, ax1);
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n = 19
ax0, ax1 = plot_puzzle(hma, n)

# patterns 
plot_ptrn('Ca', -1, ax1);
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n = 20
ax0, ax1 = plot_puzzle(hma, n)

# patterns 
plot_ptrn('Pb', -1, ax1);
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Ok, that is it. Let's try to summarize what we have learned...

Summary

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from maxrf4u import plot_patterns, get_patterns, DataStack 
from maxrf4u.peakmaps import _add_hotlines_ticklabels

ds = DataStack('RP-T-1898-A-3689.datastack')

x_keVs = ds.read('maxrf_energies') 
y_max = ds.read('maxrf_maxspectrum')
y_sum = ds.read('maxrf_sumspectrum') 
hotmax_spectra = ds.read('hotmax_spectra')

ptrn_list = get_patterns(['S', 'Ca', 'K', 'Cl', 'Fe', 'Mn', 'Cu', 'Zn', 'Pb', 'Ti', 'Ba'])

fig, [ax, ax1] = plt.subplots(nrows=2, sharex=True, figsize=[9, 5])

plot_patterns(ptrn_list, ax=ax)
_add_hotlines_ticklabels('RP-T-1898-A-3689.datastack', ax, clip_vline=False) 

#plot_cube_slices('RP-T-1898-A-3689.datastack', ax=ax1); 

ax1.plot(x_keVs, y_max, color='r', label='max spectrum') 
ax1.fill_between(x_keVs, y_max, color='r', alpha=0.3)

for y_hot in hotmax_spectra: 
    ax1.plot(x_keVs, y_hot, color=[0.2, 0.1, 0.8], linewidth=0.5) 
#ax1.plot(x_keVs, y_sum, color=[0.3, 1, 0.3], label='sum spectrum')
_add_hotlines_ticklabels('RP-T-1898-A-3689.datastack', ax1) 

ax1.set_xlim([-1, 23])
ax1.set_ylim([-5, 100])
ax1.legend();

ax.set_title('Peak pattern summary')
plt.tight_layout()
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Altogether the spectral data indicates that 11 chemical elements are present in the Susanna drawing: sulfur (S), chlorine (Cl), potassium (K), calcium (Ca), barium (Ba), titanium (Ti), manganese (Mn), iron (Fe), copper (Cu), zinc (Zn) and lead (Pb).

In the next section we will look into the spatial distribution of these elements...

FUNCTIONS

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get_patterns[source]

get_patterns(elements=None, tube_keV=30, color_select=None)

Returns pattern dict list for `elements` list, sorted according to alpha peak energy.

By default all elements are colored with a standard color. To colorize only specific elements,
provide a list of elements `color_select`.
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colorize[source]

colorize(elem)

Pick fixed color from nice color map for elements of interest.
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plot_ptrn[source]

plot_ptrn(elem, y, ax, color_select=None)

Low level plot element pattern at level `y` in axes `ax`.
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plot_patterns[source]

plot_patterns(elements=None, instr_ptrn_from_datastack_file=None, color_select=None, ax=None)

Wrapper function to plot overview of `element` and instrument patterns in axes `ax`.

Returns: `ax`
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plot_puzzle[source]

plot_puzzle(datastack_file, n, elements=None, color_select=None, footspace=0.2)

Plot peak pattern puzzle for hotmax spectrum `n` with emission patterns.

If `elements` is specified, only plot patterns for those elements.
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get_instrument_pattern[source]

get_instrument_pattern(datastack_file)

Generate instrument peak pattern.

Pattern dictionary contains strongest Rhodium anode emission peaks,
their corresponding Compton shifted peaks, and a sensor peak

Returns: instrument_pattern_dict
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add_hotlines[source]

add_hotlines(datastack_file, ax, vlines=True, clip_vline=True)

Utility function. Adds hotlines and tick labels to plot `ax`.

Instrument peaks are colored black.
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